Gather list elements by labels

I believe the best way is to use an Ordering function with recognition of duplicates.
Please see that (self) Q&A for an explanation.

myOrdering[a_List] := GatherBy[Ordering@a, a[[#]] &]

list[[#]] & /@ myOrdering[labels]

{{{1, 2}, {-3, 4}, {-9, 1}}, {{5, 6}, {7, 8}}, {{-1, 3}, {0, 1}}}

Benchmarking

And updated benchmark for recent versions, performed in 10.1.0.

Note: in version 7 Pick was orders of magnitude slower in this test. Now it is competitive but it still falls behind as the number of unique labels increases.

myOrdering[a_List] := GatherBy[Ordering@a, a[[#]] &]

f1[{list_, labels_}] :=
  Extract[list, Position[labels, #]] & /@ Union@labels

f2[{list_, labels_}] :=
  Pick[list, labels, #] & /@ Union@labels

f3[{list_, labels_}] :=
  GatherBy[Sort[Transpose@{labels, list}, OrderedQ[{#1[[1]], #2[[1]]}] &], 
   First][[All, All, 2]]

f4[{list_, labels_}] :=
  Reap[MapThread[Sow, {list, labels}], Union@labels][[2, All, 1]]

f5[{list_, labels_}] :=
  list[[#]] & /@ myOrdering[labels]

g[n_] := RandomInteger[⌈n/4⌉, #] & /@ {{n, 2}, n}


Needs["GeneralUtilities`"]

BenchmarkPlot[{f1, f2, f3, f4, f5}, g, 10]

enter image description here


I'm always afraid in case of list-manipulation that there was a duplicate in the past. But I do not remember.

You can try this:

Extract[list, Position[labels, #]] & /@ Union@labels

{{{1 ,2}, {-3, 4}, {-9, 1}}, {{5, 6}, {7, 8}}, {{-1, 3}, {0, 1}}}

and this:

Pick[list, labels, #] & /@ Union@labels

{{{1, 2}, {-3, 4}, {-9, 1}}, {{5, 6}, {7, 8}}, {{-1, 3}, {0, 1}}}

GatherBy variation 

GatherBy[Sort@Thread[Rule[labels, list]], First][[ ;; , ;; , 2]]

{{{-9, 1}, {-3, 4}, {1, 2}}, {{5, 6}, {7, 8}}, {{-1, 3}, {0, 1}}}


My GatherBy variation:

GatherBy[Transpose@{labels, list}, First][[All, All, 2]]

{{{1, 2}, {-3, 4}, {-9, 1}}, {{-1, 3}, {0, 1}}, {{5, 6}, {7, 8}}}

A possible drawback is that the result is not sorted by label. This is easy to change by doing

GatherBy[Sort@Transpose@{labels, list}, First][[All, All, 2]]

{{{-9, 1}, {-3, 4}, {1, 2}}, {{5, 6}, {7, 8}}, {{-1, 3}, {0, 1}}}

which sorts by label but destroys the initial intra-label ordering or by

GatherBy[Sort[Transpose@{labels, list}, OrderedQ[{#1[[1]], #2[[1]]}] &], First][[All, All, 2]]

{{{1, 2}, {-3, 4}, {-9, 1}}, {{5, 6}, {7, 8}}, {{-1, 3}, {0, 1}}}

which keeps the initial order.

Tags:

Sorting

List Manipulation

Gathering

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